Mathematical and Empirical Models

Abstract

Traffic models are very useful for various purposes. First, they can help in the design and operations of traffic systems since they can predict traffic operational conditions at some time in the future under various sets of design, traffic, and control characteristics. Traffic engineers and designers can make decisions regarding facility modifications or traffic management improvements based on the expected impact of those improvements in the transportation system. Second, they can help in the evaluation of existing systems and in the development of priorities for improvement. Mathematical models are those that describe a physical system mathematically. Such models describe specific relationships. For example, Flow = Speed × Density is a mathematical model. Empirical models are those based on field observations (empirical observations) rather than on relationships that can be mathematically described. Empirical models predict how a system behaves rather than explaining how its components interact. Empirical models can be very useful when the mathematical relationship is unknown or very difficult to express. Examples of empirical models are the traffic stream relationships discussed in Chap. 3.

Problem

• 1. Conduct a literature review and discuss comparisons between shockwave analysis and queuing analysis. Do the two analysis methods provide consistent results? What are differences between the two methods?